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Thermal conductivity of disordered lattices in the weak coupling regime

Huveneers, François (2012), Thermal conductivity of disordered lattices in the weak coupling regime. https://basepub.dauphine.fr/handle/123456789/9428

Type
Document de travail / Working paper
Date
2012
Series title
Université Paris-Dauphine
Published in
Paris
Pages
20
Metadata
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Author(s)
Huveneers, François
Abstract (EN)
We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.
Subjects / Keywords
Weak interactions (Nuclear physics); Heat -- Transmission